Coercive combined field integral equations

Coercive combined field integral equations

Regularized Combined Field Integral Equations

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...

Intrinsic ferroelectric coercive field

The Landau-Ginzburg theory of ferroelectricity predicts the intrinsic coercive field for polarization reversal, but the observed extrinsic coercive field is always much smaller as a result of nucleation, dynamic processes not covered by the static theory. We have realized the intrinsic coercive field for the first time, in two-dimensional Langmuir-Blodgett polymer films as thin as 1 nm. The mea...

Mean-Field Backward Stochastic Volterra Integral Equations

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

Generalized Combined Field Integral Equations for the Iterative Solution of the Helmholtz Equation in Three Dimensions

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of acoustic scattering problems. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the wel...